Three Commonly Used Probability Distributions
for Discrete Random Variables
Dist
Random Var.
Possible
Values
Probability
Distribution
Para
meters
Mean
Var
Binomial
r.v. X =
number of
successes in
n
independent
trials
X=
0,.
..,n
N
x
p
p
x
N
x


(
)
1
n=
#trials
p=
P(succ
ess)
np
np(1p)
Geomet
ric
r.v. X =
number of
failures until
first success
X =
1,2,.
.
(
29
1
1


p
p
x
p=
P(succ
ess)
1
p
(
29
1
2

p
p
Poisson
r.v. X =
number of
events in the
interval
X =
0, 1, .
..
f x
e
x
x
(
)
!
=

λ
λ
=E(X)
λ
λ
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•
10% of fires calls are false alarms. Find the
probability that, out of 5 calls, there are 5
real fires.
•
10% of fires calls are false alarms. Find the
probability of exactly 6 calls to the first
false alarm.
•
On average 3.2 fire calls are received per
hour.
Find the probability that at least one
call is received in an hour.
•
1% of components are defective.
I sample
5.
Find the probability of at least one
defective in the sample.
2
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 Spring '09
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